Vertex Of Cone Research Articles

Renormalization of translated cone exchange transformations

In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a geometric construction for the first return map to a neighbourhood of the vertex of the middle cone for a large class of parameters, then we show a recurrence in the first return map tied to Diophantine properties of the parameters, and subsequently prove the infinite renormalizability of the first return map for these parameters.

A semi-analytical spectral element model for guided wave propagation in composite laminated conical shells

The conical shell is a typical non-uniform waveguide with its circumferential radius varies linearly. This work aims to provide physical insights for the composite laminated conical shell in terms of waves. A semi-analytical spectral element model is presented, which adopts the Fourier series in the circumferential direction and the higher-order shape functions in the axial direction. The first-order shear deformation theory and Hamilton principle are employed to derive the energy functions of the conical shell, and they are discretized using the spectral elements to achieve a weak-form variational problem. The dispersion equation and the group velocity expression are derived via the piecewise approximation concept and Bloch's periodic theorem. The accuracy of the developed spectral element is verified by comparison with published results. The deformation evolution mechanisms of the composite conical shell are revealed, and the wave propagation characteristics of uniform and ply drop-off composite conical shells are investigated. The results demonstrated that wavenumber distribution at 0–5 kHz is spatially dependent, and wavenumber becomes cut off and bifurcate near the cone vertex. When the frequency exceeds 2 kHz, the deformation of conical shell changes from rigid to flexible, and the structure tends to be a uniform waveguide. Compared to the geometric curvature effect, the asymmetric lay-up leads to more significant mode coupling.

Optimisation of calibration parameters for a discrete element method (DEM) model of plant-origin grains with a low elasticity modulus

This paper presents the application of the Discrete Element Method (DEM) to describe the physical properties of plant-origin grains with a low elasticity modulus for the needs of numerical simulation of processing processes. The study proposes the modelling of maize grains based on 3D scanning of real grains and further use of the multi-sphere method to fill the numerical model with a conglomerate of elementary spheres. The main aim of the paper is to develop a calibration method based on exploring parameter spaces at points selected using Sobol's grids. As criteria and functional limitations for the calibration, the following were proposed: the slope angle of repose (AoR), the radius of the heaped cone's vertex (Rad), the number of grains, and the slope height. The study results show that for the calibration of the DEM model describing maize grains, test points with a set of the following nine parameters should be used: Poisson's Ratio for grain, Density of grain, Shear Modulus, Coefficient of Restitution for grain-grain, Coefficient of Restitution for grain-material, Coefficient of static friction for grain- grain, Coefficient of static friction for grain-material, Coefficient of rolling friction for grain-grain, and Coefficient of rolling friction for grain-material.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Optimal design and evaluation for sphere capsules in the packed bed latent thermal energy storage

The high-performance PLTES basically relies on the heat transfer inside the sphere capsule. To achieve a high cost-performance enhancement, the sphere capsule with the copper foam partially filled is proposed, depending on the full utilization of the foam enhancement and natural convection. The melting performance of the partly filled sphere capsule and the optimization, including the geometric shape and foam material usage, is numerically investigated. The economic assessment of these initial cases and the optimized cases is also conducted to evaluate the economic feasibility. The numerical results indicate the partially filled strategy is effective and the optimal design is the spherical capsule with a copper foam geometric shape that resembles a high cone with a prominent center. This is because the buoyancy-driven natural convection is fully used to enhance the heat transfer in the upper section and the foam is used to enhance the heat transfer in the bottom section. Based on this analysis, a better effect can be obtained by maintaining consistent angle size while changing the height of the vertex of the high cone. Through this optimization, the usage of copper foam is reduced by 24.48 % at the same melting rate.

Solutions with exponential singularity for (3 + 1)-D Protter problems

In the 1950s, Protter proposed multi-dimensional analogues of the classical Guderley–Morawetz problem for mixed-type hyperbolic-elliptic equations on the plane that models transonic flows in fluid dynamics. The multi-dimensional variants turn out to be different from the two-dimensional case and the situation there is still not clear. Here, we study Protter problems in the hyperbolic part of the domain. Unlike the planar analogues, the four-dimensional variant is not well-posed for classical solutions. The problem is not Fredholm — there is an infinite number of necessary conditions for classical solvability. Alternatively, the notion of a generalized solution that may have singularities was introduced. It is known that for smooth right-hand sides, the uniquely determined generalized solution may have a power-type growth at one boundary point. The singularity is isolated at the vertex of the boundary characteristic light cone and does not propagate along the cone. Here, we construct a new singular solution with an exponential growth at the point where the singularity appears.

Development and Research of a Medium Vertical Dipole Electromagnetic Pulse Simulator

In this paper, the design of a self-developed EMP simulator with a 5 m height and an inverted conducting mono-cone antenna with a cone half-angle of 32° is introduced. The experimental region of the simulator is a circular area of 25 m in diameter around the cone vertex. Two feeding modes, feed-in over the ground and feed-in under the ground, are realized by two different high-voltage pulse sources. It can be concluded through radiation field testing that the radiation field waveform generated by the simulator has a rise time of 2–3 ns and a half-width of about 25 ns, meeting the specifications of the EMP experimental waveform in the IEC61000-2-9 standard. Meanwhile, the differences between the engineering implementation of the simulator and its ideal structure during the design process can lead to some distortion issues in the antenna radiation characteristics and the electromagnetic radiation field it generates. The radiation field waveform and the distribution of the EMP field generated by the simulator under different feeding methods, antenna wire quantities, antenna end processing methods, and different antenna resistive loading were studied, and the changes in the radiation field waveform and field distribution with different angles and distances of the monitoring point were analyzed. Based on the measurement results, the radiation characteristics of the antenna and the factors that affect the waveform of the field were studied and analyzed. Through the aforementioned work, a comprehensive understanding of the performance, radiation characteristics, and engineering factors affecting the electromagnetic environment generated by the simulator has been obtained. On this basis, the parameters of the antenna wire quantity, antenna end processing method, and test point position of the designed simulator were reconfirmed and optimized. In summary, this work has important reference significance for mastering the development technology of such simulators, understanding their antenna radiation characteristics, and conducting EMP-related assessments and effect experiments in the future.

SMEFTs living on the edge: determining the UV theories from positivity and extremality

We study the “inverse problem” in the context of the Standard Model Effective Field Theory (SMEFT): how and to what extend can one reconstruct the UV theory, given the measured values of the operator coefficients in the IR? The main obstacle of this problem is the degeneracies in the space of coefficients: a given SMEFT truncated at a finite dimension can be mapped to infinitely many UV theories. We discuss these degeneracies at the dimension-8 level, and show that positivity bounds play a crucial role in the inverse problem. In particular, the degeneracies either vanish or become significantly limited for SMEFTs that live on or close to the positivity bounds. The UV particles of these SMEFTs, and their properties such as spin, charge, other quantum numbers, and interactions with the SM particles, can often be uniquely determined, assuming dimension-8 coefficients are measured. The allowed region for SMEFTs, which forms a convex cone, can be systematically constructed by enumerating its generators. We show that a geometric notion, extremality, conveniently connects the positivity problem with the inverse problem. We discuss the implications of a SMEFT living on an extremal ray, on a k-face, and on the vertex of the positive cone. We also show that the information of the dimension-8 coefficients can be used to set exclusion limits on all individual UV states that interact with the SM, independent of specific model assumptions. Our results indicate that the dimension-8 operators encode much more information about the UV than one would naively expect, which can be used to reverse engineer the UV physics from the SMEFT.

Irreversibility analysis for Casson thermo‐fluidics inside a cone: Cattaneo–Christov heat flux

AbstractIn this communication, thermodynamic irreversibility arising in dissipative Casson fluid flow inside a cone is investigated. The boundary–layer flow is considered wherein the motion is caused due to a point sink at the cone's vertex and the movement of the wall of the cone. The wall of the cone is subjected to mass transpiration that alters the flow and thermal regime. The cone having fluid‐saturated porous medium experiences Cattaneo–Christov heat flux. The configuration admits a similarity transformation that yields a boundary value problem (BVP) comprising an ordinary differential equation. The BVP is treated by the fourth‐order R‐K method along with the shooting algorithm. The system yields a dual solution for momentum and energy, which gives rise to a dual regime for entropy distribution. Numerical computations provide quantities of interest viz. velocity and temperature distributions, skin friction coefficient, Nusselt number, and entropy distribution. Phenomena exhibited through profiles/tables for velocity, temperature, entropy, streamlines, and other quantities of interest reveal interesting results.

An Automatic 3D Point Cloud Registration Method Based on Biological Vision

When measuring surface deformation, because the overlap of point clouds before and after deformation is small and the accuracy of the initial value of point cloud registration cannot be guaranteed, traditional point cloud registration methods cannot be applied. In order to solve this problem, a complete solution is proposed, first, by fixing at least three cones to the target. Then, through cone vertices, initial values of the transformation matrix can be calculated. On the basis of this, the point cloud registration can be performed accurately through the iterative closest point (ICP) algorithm using the neighboring point clouds of cone vertices. To improve the automation of this solution, an accurate and automatic point cloud registration method based on biological vision is proposed. First, the three-dimensional (3D) coordinates of cone vertices are obtained through multi-view observation, feature detection, data fusion, and shape fitting. In shape fitting, a closed-form solution of cone vertices is derived on the basis of the quadratic form. Second, a random strategy is designed to calculate the initial values of the transformation matrix between two point clouds. Then, combined with ICP, point cloud registration is realized automatically and precisely. The simulation results showed that, when the intensity of Gaussian noise ranged from 0 to 1 mr (where mr denotes the average mesh resolution of the models), the rotation and translation errors of point cloud registration were less than 0.1° and 1 mr, respectively. Lastly, a camera-projector system to dynamically measure the surface deformation during ablation tests in an arc-heated wind tunnel was developed, and the experimental results showed that the measuring precision for surface deformation exceeded 0.05 mm when surface deformation was smaller than 4 mm.

Research on the parameter analysis of combined focusing of right Angle cone and projectile

In a sound wave measurement engineer, a combination focusing device of right angle cone and parabola was designed to increase the emission sound pressure, and by exploring and simulating the relationship between the position and size of the spherical focus area and the height of the right-angled cone, the position of the apex of the right-angled cone, the focal length of the parabolic and other parameters. The analytical relationship between each parameter and the sound pressure level of the spherical area focused at a certain position from the vertex of the right-angled cone is obtained.

On joint probability distribution of the number of vertices and area of the convex hulls generated by a Poisson point process

Consider a convex hull generated by a homogeneous Poisson point process in a cone in the plane. In the present paper the central limit theorem is proved for the joint probability distribution of the number of vertices and the area of a convex hull in a cone bounded by the disk of radius T (the center of the disk is at the cone vertex), for T→∞. From the results of the present paper the previously known results of Groeneboom (1988) and Cabo and Groeneboom (1994) are followed, in which the central limit theorem was proved for the number of vertices and the area of the convex hull in a square by approximating the binomial point process by a homogeneous Poisson point process.

Tilings of Convex Polyhedral Cones and Topological Properties of Self-Affine Tiles

Let $${\varvec{a}}_1,\ldots , {\varvec{a}}_r$$ be vectors in a half-space of $${\mathbb {R}}^n$$ . We call $$C={\varvec{a}}_1{\mathbb {R}}^{+}+\cdots +{\varvec{a}}_r {\mathbb {R}}^{+}$$ a convex polyhedral cone and $$\{{\varvec{a}}_1,\ldots , {\varvec{a}}_r\}$$ a generator set of C. A generator set with the minimal cardinality is called a frame. We investigate the translation tilings of convex polyhedral cones. Let $$T\subset {\mathbb {R}}^n$$ be a compact set such that T is the closure of its interior, and $${{\mathcal {J}}}\subset {\mathbb {R}}^n$$ be a discrete set. We say $$(T,{{\mathcal {J}}})$$ is a translation tiling of C if $$T+{{\mathcal {J}}}=C$$ and any two translations of T in $$T+{{\mathcal {J}}}$$ are disjoint in Lebesgue measure. We show that if the cardinality of a frame of C is larger than the dimension of C, then C does not admit any translation tiling; if the cardinality of a frame of C equals the dimension of C, then the translation tilings of C can be reduced to the translation tilings of $$({\mathbb {Z}}^+)^n$$ . As an application, we characterize all the self-affine tiles possessing polyhedral corners (that is, there exists a point of the tile such that a neighborhood of the point is congruent to a neighborhood of the vertex of a convex polyhedral cone), which generalizes a result of Odlyzko (Proc. Lond. Math. Soc. 37, 213–229 (1978)).

Simulation of beam steering control in arrayed liquid prisms system based on electrowetting-on-dielectric

In this paper, an arrayed liquid prisms system based on electrowetting-on-dielectric (EWOD) is proposed to modulate the three-dimensional beam steering control. The relationships between beam steering control range, electrowetting contact angle, and liquid refractive index are derived. COMSOL is employed to demonstrate the beam steering control properties of the electrowetting-based arrayed liquid prisms when bias voltages are applied. The influence of contact angle, liquid refractive index, and interval between adjacent prisms are discussed. The results show that the beam steering control performance of the system will be greatly improved, and the range of beam steering angle is −20° to 20° by selecting optimum combinations of liquids and rational interval between adjacent prisms. The arrayed liquid prisms system can succeed to achieve continuous control of beam steering in a conical region with an apex angle of 40°, and the vertex of the circular cone is located at the 15.02 mm in the z-axis. The proposed system will promote the development of non-mechanical beam steering technology and have a wide range of applications.

Active vibration control of truncated conical shell under harmonic excitation using piezoelectric actuator

Abstract In this study, active vibration control of an FGM truncated conical shell, subjected to the harmonic excitation, is investigated via a semi-analytical method. The governing equations of truncated conical shells in conjunction with piezoelectric layers are derived using Donnell shell theory and von Karman's non-linearity. Then, the dynamic equation of the system is discretized using Galerkin method to obtain the ordinary differential equation of system. Using the semi-analytical method by means of perturbation theory, the frequency response of superharmonic and sub-harmonic analysis of the system is performed. Then, using the piezoelectric smart materials, the active vibration control for the truncated conical shell is investigated and frequency-amplitude functions are analyzed for the superharmonic and subharmonic resonances. The results presents the influence of excitation amplitude and cone vertex angle on the frequency-amplitude response and in specific the effect of different control gain coefficients on the system's vibration behavior. Finally, the performance of active control strategy is investigated by means of the time response of system equipped with piezoelectric layers for different types of the FG distribution in thickness direction.

Ultraheavy and Ultrarelativistic Dirac Quasiparticles in Sandwiched Graphenes.

Electrons in quantum materials exhibiting coexistence of dispersionless (flat) bands piercing dispersive (steep) bands give rise to strongly correlated phenomena and are associated with unconventional superconductivity. We show that in twisted sandwiched graphene (TSWG)-a three-layer van der Waals heterostructure with a twisted middle layer-steep Dirac cones can coexist with dramatic band flattening at the same energy scale, if twisted by 1.5°. This phenomenon is not stable in the simplified continuum models. The key result of this Letter is that the flat bands become stable only as a consequence of lattice relaxation processes included in our atomistic calculations. Further on, external fields can change the relative energy offset between the Dirac cone vertex and the flat bands and enhance band hybridization, which could permit controlling correlated phases. Our work establishes twisted sandwiched graphene as a new platform for research into strongly interacting two-dimensional quantum matter.

Conical singular points and vector fields

In this article, several examples of mechanical systems which configuration spaces are smooth manifolds with a unique singular point are considered. Configuration spaces are the following: two smooth curves with a common point (or tangent) on the two-dimensional torus, four smooth curves on the four-dimensional torus with a common point, twodimensional cone (cusp) in the space R6. The main problem in the article is the calculation of (co)tangent space at a singular point by using different theoretical approaches. Outside of the singular point, the motion could be described in the frames of classical mechanics. But in the neighborhood of the singular points the terms like “tangent vector” and “cotangent vector” must have new conceptual definitions. In this article, the approach of differential spaces is used. Two differential structures for the modeling conical singular point are studied in order to construct (co)tangent space at singular points: locally-constants functions near to the cone vertex and the algebra of the restrictions of smooth functions in the comprehensive Euclidean space on the cone. In the first case, tangent and cotangent spaces at the singular points are zero. In the second case, the value of the functions on the cotangent bundle is constant on the cotangent layer under the singular point.

Tooth contact analysis with latent error of double circular-arc spiral bevel gears for industrial robot joint nutation drive

The influence of the cone vertex error and tilt error on the tooth contact trace of double circular-arc spiral bevel gears for industrial robot joint nutation drive has been studied in this paper. According to the meshing relationship between double circular-arc spiral bevel gear and crown gear, the meshing coordinate systems with latent error parameters of cone vertex error and tilt error were established, and the tooth profile equations of external and internal spiral bevel gears were deduced. According to the meshing equation and coordinate transformation, the contact trace equation of the tooth surface was established, and the influence of different latent error values on the location of the contact trace was solved and analyzed. The finite element loading contact simulation of the double circular-arc spiral bevel gears with different latent error values was carried out. The results of the simulation analysis and numerical analysis were basically consistent. The latent errors would cause noise and vibration of industrial robot joint nutation drive and affect the service life of double circular-arc spiral bevel gears.

Characterization of the effects of detector angular misalignments and accuracy enhancement of X-ray CT dimensional measurements

Characterization of the effects of detector angular misalignments and accuracy enhancement of X-ray CT dimensional measurements

Normed Planes in Tangent Cone to Chord Space of Nonpositive Curvature

We continue the cycle of papers devoted to study of the geometry of Busemann’s G-spaces with a distinguished family of segments (so-called chord spaces) which have non-positive curvature with respect to this family. We study the geometry of the tangent cone to chord space with non-positive curvature. It is shown that any two straight lines passing through the vertex of the cone span a weak normed plane, i.e., a weakly convex subset isometric to a plane with some norm.